Last week I watched films in which chicks snog each other before being hacked to pieces (Lesbian Vampire Killers), women are kidnapped (Punisher: War Zone) or relegated to naked non-speaking extras (Valhalla Rising), and Oscar-winning actresses are reduced to the slutty denizens of one man's harem (Nine). I've also watched or rewatched a lot of anime, in which girls pilot giant robots, hunt down vampires or learn ninja skills. I think you can see what I'm getting at here.

For years I avoided anime because I was put off by the big saucer eyes. Then it dawned on me the faces and figures were no more stylised than in the prints of, say, Utamaro or Hokusai. It's just a way of looking at the world. The film that truly converted me, however, was Hayao Miyazaki's Spirited Away, in which a 10-year-old girl has the oddest, most captivating adventure since Alice in Wonderland.

In the films of Studio Ghibli (co-headed by Miyazaki), girls and women aren't also-rans, as they are in 99% of Hollywood output; they fly gliders, run with wolves or design seaplanes. Even ordinary schoolgirls lead lives of quiet enchantment, like 14-year-old Shizuku in Whisper of the Heart, who discovers first love and a talent for storytelling in a Tokyo setting that is simultaneously realistic and magical. Where were these heroines when I was growing up? I had to make do with Lady Penelope.

Beyond Ghibli, even male-centric anime, such as the ninjas-in-training Naruto, feature gutsy girls like pink-haired Sakura, who starts off drippy but toughens up as the series goes on. "Girls need to be strong to survive," she says.

As far as I'm aware, all the anime I've ever seen were written and directed by men. With sexism more ingrained in Japanese society than our own, it's perhaps not surprising so many female characters in adult-orientated anime are objectified – even as their actions give them an independence not often granted to women in Hollywood blockbusters. Major Kusanagi, the big-bosomed bionic heroine of Mamoru Oshii's mesmerising Ghost in the Shell (one of the inspirations for The Matrix and a plot I'm still unable to fathom, even after repeated viewings) is frequently nude or leaping around in a form-fitting bodysuit that makes her look naked. Maybe she is a male fetish object – but hey, I dig her, too. Faye Valentine, the gambler in the sci-fi noir-western anime Cowboy Bebop (almost a dry run for Joss Whedon's Firefly) wears va-va-voom hotpants and crop-top – not the most practical gear for a spaceship, though it doesn't stop her being funny and feisty.

More ambiguous is the sexual presen-tation of Neon Genesis Evangelion's Misato Katsuragi, a strict lady scientist with a party-animal domestic life, who frequently thrusts bosom or bottom at Shinji, the schoolboy pilot of a giant robot protecting the remains of civilisation; but these glimpses are from Shinji's point of view, and she's one of a lineup in which girl pilots and scientists outnumber their male counterparts.

In the case of Satoshi Kon's Perfect Blue (J-pop noir thriller in the style of Dario Argento), the hallucinatory sexual violence is as much commentary of the objectification of young female celebrities as a part of its protoganist's mental journey. Kon's follow-up, Millennium Actress, couldn't be more chaste, however, a tale of unrequited love played out via the history of Japanese cinema, with a central character clearly inspired by actress Setsuko Hara, who worked with Ozu, Kurosawa and Naruse, all of whose directing styles Kon references.

If I had a small daughter, I would try to wean her away from Edward Cullen and Miley Cyrus and towards such anime series as the thrilling steampunk saga Nadia: Secret of Blue Water – inspired by Jules Verne, conceived by Miyazaki and featuring a 14-year-old lion tamer/acrobat in 1889 Paris. And I would teach her to read subtitles, so she wouldn't have to settle for naff dubbed versions. You want strong female role models? Anime's got them in spades.